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Showing papers on "Fracture (geology) published in 1973"


Book
01 Jan 1973
TL;DR: In this article, the authors introduce the concept of a crack extension force which can be used to rank materials in some order of fracture resistance and determine the largest crack that a material will tolerate without failure.
Abstract: It is weH known that the traditional failure criteria cannot adequately explain failures which occur at a nominal stress level considerably lower than the ultimate strength of the material. The current procedure for predicting the safe loads or safe useful life of a structural member has been evolved around the discipline oflinear fracture mechanics. This approach introduces the concept of a crack extension force which can be used to rank materials in some order of fracture resistance. The idea is to determine the largest crack that a material will tolerate without failure. Laboratory methods for characterizing the fracture toughness of many engineering materials are now available. While these test data are useful for providing some rough guidance in the choice of materials, it is not clear how they could be used in the design of a structure. The understanding of the relationship between laboratory tests and fracture design of structures is, to say the least, deficient. Fracture mechanics is presently at astandstill until the basic problems of scaling from laboratory models to fuH size structures and mixed mode crack propagation are resolved. The answers to these questions require some basic understanding ofthe theory and will not be found by testing more specimens. The current theory of fracture is inadequate for many reasons. First of aH it can only treat idealized problems where the applied load must be directed normal to the crack plane.

629 citations



Journal ArticleDOI
G.C. Sih1
TL;DR: In this paper, the authors re-examine some of the fundamental concepts of the classical theory of fracture and discuss the numerous inconsistencies and misconceptions that have not received attention, and apply the modified Griffith theory for ductile material.

487 citations


Book ChapterDOI
01 Jan 1973
TL;DR: In this article, a finite element solution to the large-scale yielding of a circumferentially cracked round tension bar is obtained, and the three-dimensional aspects of flawed structures and numerical methods of treating them are studied.
Abstract: Numerical procedures for accurate determination of elastic stress intensity factors for the general two-dimensional crack problem are reviewed. The elastic perfectly plastic state of crack tip deformation is studied by a finite element procedure. Elastic-plastic fields in the immediate vicinity of a crack tip are determined numerically by finite element procedures based on asymptotic studies of crack tip singularities in plastic materials. The small-scale yielding problem is modeled, and expressions for crack tip opening displacement, shear singularity amplitude, and plastic zone extent are derived. A finite element solution to the large-scale yielding of a circumferentially cracked round tension bar is obtained. The three-dimensional aspects of flawed structures and numerical methods of treating them are studied. Ductile fracture mechanisms, in particular crack tip fracture on the microscale, are discussed.

290 citations


Journal ArticleDOI
TL;DR: In this paper, a fracture mechanics approach was used to investigate the high strength of hot-pressed Si3N4 powders, and room-temperature flexural strengths, fracture energies, and elastic moduli were determined for material fabricated from α- and β-phase Si3 N4 powder.
Abstract: A fracture mechanics approach was used to investigate the high strength of hot-pressed Si3N4. Room-temperature flexural strengths, fracture energies, and elastic moduli were determined for material fabricated from α- and β-phase Si3N4 powders. When the proper powder preparation technique was used, α-phase powder resulted in a high fracture energy (69,000 ergs/cm2), a high flexural strength (95,000 psi), and an elongated (fiberlike) grain morphology, whereas β-phase powder produced a low fracture energy (16,000 ergs/cm2), a relatively low strength (55,000 psi), and an equiaxed grain morphology. It was hypothesized that the high strength of Si3N4 hot-pressed from α-phase powder results from its high fracture energy, which is attributed to the elongated grains. High-strength Si3N4 has directional properties caused, in part, by the elongated grain structure, which is oriented preferentially with respect to the hot-pressing direction.

274 citations


Journal ArticleDOI
01 Aug 1973
TL;DR: In this paper, the authors measured the fracture resistance of Salem limestone measured in terms ofR, the energy dissipated per unit area of projected surface, was found to increase in the initial stage of crack extension but finally reached a constant value which was strongly dependent on crack orientation with respect to the bedding plane.
Abstract: Influence of Microstructure on Fracture Propagation in Rock This paper describes the results of research to correlate the fracture resistance with microstructural features of Salem limestone and Berea sandstone. Tests were conducted on wedge-loaded double-cantilever-beam specimens containing machined slots as crack starters. The fracture resistance of Salem limestone measured in terms ofR, the energy dissipated per unit area of projected surface, was found to increase in the initial stage of crack extension but finally reached a constant value which was strongly dependent on crack orientation with respect to the bedding plane. For this limestoneR ranges from about 50 joules/m2 to 230 joules/m2 (1 joule/m2 = 104 erg/cm2). The sandstone which is a more compliant rock exhibited similar fracture behavior while theR values ranged from 465 joules/m2 to 1580 joules/m2. In addition, tests in liquid nitrogen which were aimed at eliminating plastic deformation in the rocks during fracture showed little difference inR for the limestone but a substantial reduction inR for the sandstone which, in the latter case, may be caused by differential thermal expansion between the quartz grains and the calcite cement. Acoustic emissions were detected in both rocks at very early stages in the tests indicating the occurrence of microcracking near the initial slot tip at low loads. The mode of fracture and the fracture path in both materials were identified by fractography over a broad range of magnifications. The evidence gained from this work strongly points to the existence of an extensive array of microcracks produced in a region surrounding the main crack tip and which advances with it. The energy dissipated in fracturing of rock is associated with the creation of the large amount of surface area contained in this microcrack array. This picture provides a self-consistent explanation for the puzzling discrepancy between the measured tensile strength of rocks and the strengths predicted from measuredR values.

257 citations


Journal ArticleDOI
L. B. Freund1
TL;DR: In this paper, the authors determined the stress intensity factor of a half-plane crack extending non-uniformly in an isotropic elastic solid subjected to stress wave loading.
Abstract: T he stress intensity factor of a half-plane crack extending non-uniformly in an isotropic elastic solid subjected to stress wave loading is determined. A plane stress pulse strikes the crack at time t = 0, the wavefront being parallel to the plane of the crack. At some arbitrary later time t = τ, the crack begins to extend at a non-uniform rate. It is found that the stress intensity factor is a universal function of instantaneous crack-tip velocity times the stress intensity factor for an equivalent stationary crack. An energy rate balance fracture criterion is applied to obtain an equation of motion for the crack tip. The delay time between the arrival of the incident pulse and the onset of fracture is also calculated for this fracture criterion.

212 citations


Journal ArticleDOI
07 Sep 1973-Science
TL;DR: This deformation and fracture of high polymers is well known book in the world, of course many people will try to own it and this is it the book that you can receive directly after purchasing.
Abstract: Why should wait for some days to get or receive the deformation and fracture of high polymers book that you order? Why should you take it if you can get the faster one? You can find the same book that you order right here. This is it the book that you can receive directly after purchasing. This deformation and fracture of high polymers is well known book in the world, of course many people will try to own it. Why don't you become the first? Still confused with the way?

176 citations


Journal ArticleDOI
C.E. Cooke1

160 citations


Journal ArticleDOI
TL;DR: In this paper, a finite-element method has been extended for the description of growth phenomena at a crack tip in plane stress and the necessary introduction of hereditary properties of elastic-plastic stiffnesses has been carried out as well as the inclusion of routines for relaxation of cohesive crack-tip forces.
Abstract: In this paper, finite-element methods have been extended for the description of growth phenomena at a crack tip in plane stress. The necessary introduction of hereditary properties of the elastic-plastic stiffnesses has been carried out as well as the inclusion of routines for relaxation of cohesive crack-tip forces. Simple macroscopic models of the fracture process are discussed and the crack-tip opening angle is chosen for determination of a fracture criterion in the finite-element model. Under the somewhat arbitrary assumption of a constant crack opening-angle as a fracture criterion, results are obtained that make clear the possibility of simulating stable crack-growth with this method, particularly in connection with fracture toughness tests in the non-linear range. The further extension of the model for the achievement of quantitative results is also discussed.

113 citations


Journal ArticleDOI
TL;DR: In this paper, a fracture mechanical analysis has been developed to account for the observed dependence of the energy/unit area (w) on the notch size, and a correction factor (φ) has been derived to accommodate notch effects.
Abstract: Previous work on impact testing has shown that the energy/unit area (w) normally measured in notched impact tests is dependent on specimen geometry. A fracture mechanical analysis has now been developed to account for the observed dependence ofw on notch size. A correction factor (φ) has been derived to accommodate notch effects and this allows for the calculation of the strain energy release-rateG directly from the measured fracture energies. Tests on PMMA have shown that “corrected” results are independent of specimen geometry and theG c for PMMA has been evaluated as 1.04 × 103 J m−2. The experimental results show that there is an additional energy term which must be accounted for and this has been interpreted here as being due to kinetic energy losses in the specimens. A conservation of momentum analysis has allowed a realistic correction term to be calculated to include kinetic energy effects and the normalized experimental results show complete consistency between all the geometries used in the test series. It is concluded that the analysis resolves many of the difficulties associated with notched impact testing and provides for the calculation of realistic fracture toughness parameters.

Journal ArticleDOI
TL;DR: A free-air gravity map of the Guiana Basin between 15° N. and 6° S. in the western equatorial Atlantic, using all available shipboard and pendulum data, is presented in this paper.
Abstract: A free-air gravity map of the Guiana Basin between 15° N. and 6° S. in the western equatorial Atlantic, using all available shipboard and pendulum data, is presented. The gravity field is interpreted in terms of short wave-length components directly related to topographic features and a long wave-length regional field which is independent of surface or basement relief. The regional field is negative throughout the survey area, varying from −15 to −40 mgal. The magnetic anomalies over the large equatorial fracture zones indicate that the fracture zone trough is an area of zero or greatly reduced magnetization within a zone in which the magnetization is induced rather than remanent. Only about half of the gravity anomaly over the fracture zone can be assigned to topographic relief implying the presence of excess mass under the fracture zones. The gravity and magnetic evidence together suggest that large fracture zones serve as the site of intrusion of ultrabasic rocks from depth. The deformation of the lithosphere due to the sediment load of the Amazon cone and the resulting gravity anomalies were computed for various flexural rigidities, using two-dimensional elastic beam theory. The value giving the best fit to the observed gravity anomalies in both wave length and amplitude is 2 × 1023 Newton meters (nt m) (2 × 1030 dyne cm). This implies an effective lithospheric thickness of 30 km. It is suggested that the lithosphere behaves somewhat as a Kelvin (viscoelastic solid) material in its response to imposed long-term loads, approaching a minimum apparent flexural rigidity of 2 × 1030 dyne cm asymptotically in a period of a few million years.


Journal ArticleDOI
TL;DR: In this paper, the authors used a closed-loop, servocontrolled hydraulic testing machine to study the mechanisms of rock failure and found that applied load relaxes appreciably as soon as macro-cracks initiated at the specimen surfaces.

Journal ArticleDOI
TL;DR: In this paper, the effects of porosity, pore distribution, and grain size on fracture energy were evaluated and a grain-size effect dominates in dense material; the fracture energy decreases with increasing grain size.
Abstract: Alumina specimens were fabricated under a wide range of conditions using cold-pressing and sintering techniques. Fracture energies were measured by an analytical technique (notched beam) and by the Tattersall-Tappin method. Problems in using the latter method are discussed. The effects of porosity, pore distribution, and grain size on fracture energy are evaluated. Connected porosity has a deleterious effect on fracture energy. A grain-size effect dominates in dense material; the fracture energy decreases with increasing grain size.

Journal ArticleDOI
E.G. Bombolakis1
TL;DR: In this paper, an axial growth of en-echelon cleavage cracks, inclined at angles smaller than 45°, was observed in feldspar during deformation of a pegmatite having a mineralogy and texture similar to granite.

Journal ArticleDOI
TL;DR: The deformation and fracture properties of synthetic α-quartz crystals were measured using hardness, pre-cracked bend and Hertzian tests over the range 20 to 545° C in air and dry nitrogen as discussed by the authors.
Abstract: The deformation and fracture properties of synthetic α-quartz crystals were measured using hardness, pre-cracked bend and Hertzian tests over the range 20 to 545° C in air and dry nitrogen. The resistance to fracture decreases significantly with increase in temperature and is orientation-dependent (becoming very small as the inversion temperature is approached), while the microhardness remains relatively insensitive to temperature and environment. These effects are interpreted in terms of the moisture content of the environment and the intrinsic water content of the crystals.

Journal ArticleDOI
G.C. Sih1, E.P. Chen1
TL;DR: In this paper, the concept of fracture mechanics is applied to analyze the brittle fracture of unidirectional composites and the analytical prediction based on the newly developed Sc-theory agrees well with the experimental data on Scotchply 1002 where crack propagation occurs along the fiber direction.
Abstract: The concept of fracture mechanics is applied to analyze the brittle fracture of unidirectional composites. The analytical prediction based on the newly developed Sc-theory agrees well with the experimental data on Scotchply 1002 where crack propagation occurs along the fiber direction. The Sc-theory represents a departure from the classical stress-intensity factor Kc concept in that it is designed to treat the mixed mode fracture problem while the Kc-theory is limited to Mode I crack extension.

Journal ArticleDOI
TL;DR: The room-temperature fracture behavior of partially stabilized ZrO3 (PSZ) in the system CaO-ZrO2 was investigated in this paper, where fracture energy was measured using standard single-edge crack and work-of-fracture techniques.
Abstract: The room-temperature fracture behavior of partially stabilized ZrO3 (PSZ) in the system CaO-ZrO2 was investigated Fracture energy was measured using standard single-edge-crack and work-of-fracture techniques Attempts were made to relate the fracture toughness parameters to the microstructure of the material Stable crack propagation was always observed; a model is proposed to explain these observations on the basis of the formation of a microcrack zone at the tip of a propagating crack The occurrence of initial stable crack propagation is explained in terms of an increase in microcrack zone size The possibility that crack stability results from testing geometry superimposed on the microcracking stability is also discussed

Patent
18 May 1973
TL;DR: In this paper, a method of forming a fracture system in a fracturable subsurface geological formation intersecting a closed borehole including introducing a quantity of liquified gas into the closed bore hole to communicate with the fracturable formation, whereby the resulting increase in pressure exceeds the fracture pressure of the formation to form an initial group of fractures in the formation.
Abstract: A method of forming a fracture system in a fracturable subsurface geological formation intersecting a closed borehole including introducing a quantity of liquified gas into the closed borehole to communicate with the fracturable formation; allowing the quantity of liquified gas to vaporize in the closed borehole whereby the resulting increase in pressure exceeds the fracture pressure of the formation to form an initial group of fractures of a fracture system in the formation; rapidly introducing an additional quantity of liquified gas into the initial fractures in the formation; allowing the additional liquified gas in the initial fractures to rapidly vaporize therein to form a second group of fractures in the fracture system, some of which being aligned substantially normal to the initial fractures; rapidly introducing a third quantity of liquified gas through the initial fractures into the second group of fractures; and allowing the liquified gas within the second group of fractures to rapidly vaporize therein to form a third group of fractures in the fracture system, some of which being aligned substantially normal to the second group of fractures. The method also includes the steps of allowing the liquified gas in the fracture system to completely vaporize therein; allowing the pressure in the borehole to decrease relative to increased gas pressure in the formation whereby a portion of the oil in the formation is driven therefrom into the borehole; and producing the oil from the borehole to the ground surface. The method also includes introducing pressurized steam into the fracture system to thermally stimulate the flow of oil from the formation into the borehole. The method also discloses introducing air into the fracture system; and burning the oil on the fracture faces to thermally stimulate flow of oil from the formation into the borehole. The method further includes introducing pressurized steam into the fracture system to thermally stimulate flow of oil from the formation into the borehole.

Journal ArticleDOI
TL;DR: In this paper, the specific fracture energy, w/A, is derived from linear fracture mechanics by integrating well known functions for the stress field intensity factor to give the compliance and hence the work done.

Journal ArticleDOI
TL;DR: In this article, the fracture surface of impact specimens of polycarbonate tested in the range 130°C to −196°C have been studied by use of optical microscopy and scanning electron microscopy.
Abstract: The fracture surface of notched impact specimens of polycarbonate tested in the range 130°C to −196°C have been studied by use of optical microscopy and scanning electron microscopy. The morphological features associated with the initiation and propagation of fracture have been determined and interpreted in terms of the processes which occur in association with fracture, notably crazing. The fracture processes are similar to those observed in poly(methyl methacrylate) and polystyrene. The transition from ductile to brittle fracture is attributed to the case of crazing relative to shear yielding.

Journal ArticleDOI
TL;DR: In this paper, two silicon carbides with different fracture surface energies were subjected to increasingly severe thermal shock; the damage was monitored by changes in the specific damping capacity, elastic modulus, and fracture strength.
Abstract: Two silicon carbides with different fracture surface energies were subjected to increasingly severe thermal shock; the damage was monitored by changes in the specific damping capacity, elastic modulus, and fracture strength. The fracture strength followed predicted trends, but the strength losses did not correlate with the changes observed in damping and modulus. The differences in thermal-shock resistance of the materials were related to the fracture surface energy; the body with the higher fracture energy had superior resistance to thermal-shock damage.

Journal ArticleDOI
TL;DR: In this paper, the anisotropic states of stress, strain and fracture of a glass-epoxy plate containing a circular hole and subjected to uniaxial tension were analyzed.
Abstract: Experimental and finite-element analyses are presented for the anisotropic states of stress, strain and fracture of a glass-epoxy plate containing a circular hole and subjected to uniaxial tension. Strains were experimentally measured using foil gages, moire and birefringent coating. Stresses are computed in the linear range from the measured strains. While the hole reduces the plate strength by a factor of two, the maximum tensile strain at fracture is greater than the ultimate strain in a plate without a hole. Fracture consists of crack initiation at the hole boundary but off the horizontal axis. Away from the hole, failure is accompanied by considerable delamination. Discontinuous crack propagation is present.

Journal ArticleDOI
TL;DR: In this article, a comprehensive Hertzian fracture study has been made of quartz, fused silica and soda-lime glass, and two main aspects are: (i) vacuum tests, which reflect the intrinsic bond strength of the -Si-O- network, and (ii) water-environment tests, that reflect the rate processes involved in hydrolytic bond weakening.
Abstract: A comprehensive Hertzian fracture study has been made of quartz, fused silica and soda-lime glass. The two main aspects are: (i) vacuum tests, which reflect the intrinsic bond strength of the -Si-O- network, and (ii) water-environment tests, which reflect the rate processes involved in hydrolytic bond weakening. Temperature, load rate and chemical concentration are the variables investigated. The incorporation of new features into the elementary Si-O bond-rupture picture of crack extension is necessary to account for the results. In vacuum, the Hertzian fracture strength of quartz decreases dramatically as theα→β inversion temperature is approached; no such effect is evident in the non-crystalline modifications. This result is interpreted in terms of thermal oscillations of the stacking tetrahedra in the SiO2 structure. In water environments, the Hertzian strength is universally depressed, the effect becoming more pronounced at low load rates, high chemical concentrations. The physical state of the environment is an important factor in the kinetics of the hydrolytic weakening process: with the liquid state, the (thermally-activated) reaction between water molecules and crack-tip bonds is ratecontrolling; whereas with the gaseous state, it is the (temperature-insensitive) molecular diffusion along the fracture interface which controls. The secondary role of composition effects, dissipative crack-tip processes, etc., is also discussed.

Patent
02 Apr 1973
TL;DR: In this paper, a method for producing multiple fractures in earth formations in which the lines of least principal stress deviate substantially from vertical is described, and the formation adjacent the slanted borehole is hydraulically fractured at a plurality of positions along the length of the slant borehole.
Abstract: A method for producing multiple fractures in earth formations in which the lines of least principal stress deviate substantially from vertical is described. A generally vertical borehole is drilled into the formation, the formation is hydraulically fractured from the vertical borehole, the plane in which the fracture lies is determined, a slanted borehole is drilled out from the vertical borehole in a direction such that the azimuth of slanted borehole is generally perpendicular to the plane of the fracture and then the formation adjacent the slanted borehole is hydraulically fractured at a plurality of positions along the length of the slanted borehole. When the direction of lines of least principal stress is known for the formation, the steps of hydraulically fracturing from the vertical borehole and determining the plane in which the fracture lies may be omitted and the slanted borehole is drilled in the azimuth parallel to the known lines of least principal stress.

Journal ArticleDOI
TL;DR: In this paper, a conceptual model was formulated to describe crack extension at a given stress as well as the manner in which ultimate failure of concrete takes place, and compressive tests were performed on concrete prisms to investigate the nature of crack growth at the macroscopic level.

Journal ArticleDOI
TL;DR: In this paper, the effects of porosity, grain size and excess oxygen on Young's modulus and fracture strength for sintered pellets of compositions from UO2.00 to UO 2.25 were investigated at room temperature.

Patent
J Tinsley1
27 Aug 1973
TL;DR: In this paper, a fracture in a underground formation having zones of solids intermittently spaced throughout the fracture is formed by injecting alternating quantities of displacement liquid and carrier liquid having solids supported therein into the fracture to extend the fracture into the underground formation.
Abstract: A fracture in a subterranean formation having zones of solids intermittently spaced throughout the fracture is formed by injecting alternating quantities of displacement liquid and carrier liquid having solids supported therein into the fracture to extend the fracture into the subterranean formation.